/* 21.09.2008 last modification: 26.06.2013
Copyright (c) 2008-2013 by Siegfried Koepf

This file is distributed under the terms of the GNU General Public License
version 3 as published by the Free Software Foundation.
For information on usage and redistribution and for a disclaimer of all
warranties, see the file COPYING in this distribution.

k-partitions in colexicographic order

Based on Algorithm H (Partitions into m parts) in: Knuth, Donald E.: The Art of Computer Programming, Vol. 4: Fascicle 3. Generating All Combinations and Partitions. Upper Saddle River, NJ 2005.

Functions:
  int gen_k_part_colex_init(unsigned char *vector, const unsigned char n, const unsigned char k)
    Test for special cases
    Initialization of vector
    Possible return values are: GEN_ERROR, GEN_EMPTY, GEN_NEXT

  int gen_k_part_colex_next(unsigned char *vector, const unsigned char k)
    Transforms current figure in vector into its successor
    Possible return values are: GEN_NEXT, GEN_TERM

Arguments:
  unsigned char *vector; //pointer to the array where the current figure is stored
  const unsigned char n; //length of alphabet
  const unsigned char k; //length of figures

Usage and restrictions:
  Arguments and elements in vector are restricted to the interval (0, 255)
  Memory allocation for vector must be provided by the calling process
  k must be <= n

Cardinality see:
  Sloane, N.J.A. et al.: The On-Line Encyclopedia of Integer Sequences, 2008.
  http://oeis.org/A008284
*/

#include "_generate.h"

int gen_k_part_colex_init(unsigned char *vector, const unsigned char n, const unsigned char k)
{
int j; //index

//test for special cases
if(k > n)
 return(GEN_ERROR);

if(n == 0)
 return(GEN_EMPTY);

if(k == 0)
 return(GEN_ERROR);

//initialize: vector[0] = n - k + 1, vector[1, ..., k - 1] are 1
vector[0] = n - k + 1;

for(j = 1; j < k; j++)
 vector[j] = 1;

return(GEN_NEXT);
}

int gen_k_part_colex_next(unsigned char *vector, const unsigned char k)
{
int j;    //index
int r;    //temporary remainder
int temp; //auxiliary element

//terminate, this is only needed to allow k == 1
if(k <= 1)
 return(GEN_TERM);

//easy case
if(vector[1] < vector[0] - 1)
 {
 vector[0]--;
 vector[1]++;
 return(GEN_NEXT);
 }

//find leftmost element to increase and set r
r = vector[0] + vector[1] - 1;

for(j = 2; j < k; j++)
 {
 if(vector[j] < vector[0] - 1)
  break;

 r += vector[j];
 }

//terminate if no part is less than vector[0] - 1
if(j >= k)
 return(GEN_TERM);

//increase
vector[j]++;

//set left-hand elements
temp = vector[j];

for(j -= 1; j > 0; j--)
 {
 vector[j] = temp;
 r -= temp;
 }

vector[0] = r;

return(GEN_NEXT);
}